The theory of singular perturbations in the case of spectral singularities of a limit operator

A new method of asymptotic integration is developed – the method of regularization – in the case when the spectrum of the variable limit operator is zero at isolated points. To describe the singular dependence of a solution on the perturbation, additional independent variables are introduced; the space of resonance-free solutions is introduced, in which the coefficients of regularized series (the solution of the extended problem) are defined. Asymptotic convergence of the series thus obtained to the exact solution of the original singularly perturbed problem is proved.
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